Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 2003, Volume 71, Issue 4

The Time Series and Cross‐Section Asymptotics of Dynamic Panel Data Estimators

https://doi.org/10.1111/1468-0262.00441
p. 1121-1159

Javier Alvarez, Manuel Arellano

In this paper we derive the asymptotic properties of within groups (WG), GMM, and LIML estimators for an autoregressive model with random effects when both and tend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. When /→ 0 the fixed results for GMM and LIML remain valid, but WG, although consistent, has an asymptotic bias in its asymptotic distribution. When / tends to a positive constant, the WG, GMM, and LIML estimators exhibit negative asymptotic biases of order 1/, 1/, and 1/(2−), respectively. In addition, the crude GMM estimator that neglects the autocorrelation in first differenced errors is inconsistent as /→>0, despite being consistent for fixed . Finally, we discuss the properties of a random effects pseudo MLE with unrestricted initial conditions when both and tend to infinity.


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